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A critical reappraisal of some voting power paradoxes

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  • Annick Laruelle

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • F. Valenciano

Abstract

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed "natural" postulates that a measure of a priori voting power "should" satisfy, the violations of which are called "voting power paradoxes". In this paper two general measures of factual success and decisiveness based on the voting rule and the voters' behavior, and some of these postulates/paradoxes test each other. As a result serious doubts on the discriminating power of most voting power postulates are cast.
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Suggested Citation

  • Annick Laruelle & F. Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Post-Print halshs-00109411, HAL.
    • Handle: RePEc:hal:journl:halshs-00109411
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    Cited by:

    1. László Á. Kóczy, 2016. "Power Indices When Players can Commit to Reject Coalitions," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(1), pages 77-91, August.
    2. Maria Montero & Juan Vidal-Puga, 2012. "A Violation of Monotonicity in a Noncooperative Setting," Discussion Papers 2012-04, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    3. Abizadeh, Arash & Vetta, Adrian, 2024. "A recursive measure of voting power that satisfies reasonable postulates," Games and Economic Behavior, Elsevier, vol. 148(C), pages 535-565.
    4. Tobias Hiller, 2018. "The Effects of Excluding Coalitions," Games, MDPI, vol. 9(1), pages 1-7, January.
    5. László Á. Kóczy, 2009. "Measuring voting power: The paradox of new members vs the null player axiom," Working Paper Series 0903, Óbuda University, Keleti Faculty of Business and Management.
    6. Zineb Abidi & Matthieu Leprince & Vincent Merlin, 2020. "Power Inequality in Inter-communal Structures: The Simulated Impact of a Reform in the Case of the Municipalities in Western France," Post-Print halshs-02996998, HAL.
    7. Freixas, Josep & Marciniak, Dorota & Pons, Montserrat, 2012. "On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 367-375.
    8. Kóczy, L.Á., 2006. "Voting Paradoxes and the Human Intuition," Research Memorandum 048, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Freixas, Josep & Pons, Montserrat, 2008. "Circumstantial power: Optimal persuadable voters," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1114-1126, May.
    10. Arash Abizadeh & Adrian Vetta, 2021. "A Recursive Measure of Voting Power that Satisfies Reasonable Postulates," Papers 2105.03006, arXiv.org, revised May 2022.
    11. Arash Abizadeh & Adrian Vetta, 2022. "A General Framework for a Class of Quarrels: The Quarrelling Paradox Revisited," Papers 2205.08353, arXiv.org, revised Dec 2025.
    12. Arash Abizadeh & Adrian Vetta, 2022. "The Blocker Postulates for Measures of Voting Power," Papers 2205.08368, arXiv.org.
    13. Carreras, Francesc & Freixas, Josep, 2008. "On ordinal equivalence of power measures given by regular semivalues," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 221-234, March.
    14. Arash Abizadeh & Adrian Vetta, 2023. "The blocker postulates for measures of voting power," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 595-623, May.

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